A body constrained to move along Z-axis of a coordinate system which is subjected to force F given by
`F=-hati+2hatj+3hatk` N where
`hati,hatj` and `hatk` are the unit vector along the X,Y and Z axis of the system respectively. Find the work done by force F in moving the body a distance of 4 m along the Z-axis?

Options

A. 12J
B. 13J
C. 10J
D. 9J

Explanation

To find the work done by the force \( \mathbf{F} \) in moving the body a distance of 4 m along the Z-axis, we can follow these steps:

### Step 1: Identify the Force Vector
The force vector is given as:
\[ \mathbf{F} = -\hat{i} + 2\hat{j} + 3\hat{k} \text{ N} \]

### Step 2: Identify the Displacement Vector
The body moves 4 m along the Z-axis. Therefore, the displacement vector \( \mathbf{d} \) can be expressed as:
\[ \mathbf{d} = 0\hat{i} + 0\hat{j} + 4\hat{k} = 4\hat{k} \text{ m} \]

### Step 3: Calculate the Work Done
The work done \( W \) by the force when moving through a displacement is given by the dot product of the force vector and the displacement vector:
\[ W = \mathbf{F} \cdot \mathbf{d} \]

Substituting the vectors:
\[ W = (-\hat{i} + 2\hat{j} + 3\hat{k}) \cdot (0\hat{i} + 0\hat{j} + 4\hat{k}) \]

### Step 4: Compute the Dot Product
Now, we calculate the dot product:
\[ W = (-1)(0) + (2)(0) + (3)(4) \]
\[ W = 0 + 0 + 12 = 12 \text{ J} \]

### Final Answer
Thus, the work done by the force \( \mathbf{F} \) in moving the body a distance of 4 m along the Z-axis is:
\[ \boxed{12 \text{ J}} \]